In polymer physics, the tube model is typically used to model the
effect of entanglements of overlapping polymer strands [1]}.
In this model, it is assumed that the entanglements along the contour
of a chain confine the motion of the chain into a tube like region
in space and thus, predominantly the strands in contact with a given
molecule control the polymer dynamics. The situation is different
for the conformations of non-concatenated rings in melt. Any conformation
that would be concatenated needs to be expelled out of the volume
of a given ring, independent of the position of the concatenation
with respect to the ring contour. This difference is sketched in the
lower part of Figure REF . Therefore,
any model (like the tube model) that neglects concatenations in the
inner part of the (minimal) surface is not suitable to learn about
ring conformations. Conversely, the topological approach of the present
work is also not suitable to learn about the dynamics of the rings,
because all entangled strands that are not part of concatenated conformations
are not detected in our analysis and thus, would not be taken into
account to estimate the dynamics of the ring.
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